What is 2/(1-sqrt(5)) ?

The solution to 2/(1-sqrt(5)) is -(1+sqrt(5))/2

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simplify 2/(1-sqrt(5))

simplify

\frac{2}{1 - 5}

- \frac{1 + 5}{2}

Decimal Notation

- 1.61803 \dots

Solution steps

\frac{2}{1 - 5}

Multiply by the conjugate

\frac{1 + 5}{1 + 5}

= \frac{2 ( 1 + 5 )}{( 1 - 5 ) ( 1 + 5 )}

Expand

2 (1 + 5) : 2 + 25

Expand

(1 - 5) (1 + 5) : - 4

= \frac{2 + 2 5}{- 4}

Factor out common term

2 : 2 (1 + 5)

= \frac{2 ( 1 + 5 )}{- 4}

Factor the number:

4 = 2 \cdot 2

= \frac{2 ( 1 + 5 )}{- 2 \cdot 2}

Cancel the common factor:

2

= \frac{1 + 5}{- 2}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{1 + 5}{2}

4 + \frac{1}{5}

4 (6 x - 4) - 3 (5 x + 1)

(2 x - 3 x^{2}) - (6 x^{2} - 6 x)

\frac{90}{10}

\frac{3}{x} - \frac{6}{x}